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Chapter 4: Q61E (page 138)

If a laser pulse is of short enough duration, it becomes rather superfluous to refer to its specific color. How short a duration must a light pulse be for its range of frequencies to cover the entire visible spectrum? (The visible spectrum covers frequencies of -4.5to7.5×1014Hz.)

Short Answer

Expert verified

Duration must be2.65×10-16sfor the light pulse of a given range of frequencies to cover the entire visible spectrum.

Step by step solution

01

Heisenberg’s Uncertainty Principle.

Using uncertainty principle ∆E∆t≥h2

Where,∆Eis the uncertainty in energy, ∆tis the uncertainty in time,his Planck’s constant.

02

Use Heisenberg’s Uncertainty Principle for calculation.

Write is as,

∆E∆t≥h2∆hf∆t≥h2π2h∆f∆t≥h4π∆f∆t≥14π∆t≥14π∆f

Plug in the values,

∆t≥14π3×1014∆t≥2.65×10-16s

Therefore, the duration must be 2.65x10-16sfor the light pulse of a given range of frequencies to cover the entire visible spectrum.

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Most popular questions from this chapter

In Exercise 45, the case is made that the position uncertainty for a typical macroscopic object is generally so much smaller than its actual physical dimensions that applying the uncertainty principle would be absurd. Here we gain same idea of how small an object would have♦ to be before quantum mechanics might rear its head. The density of aluminum is 2.7×103 kg/m3, is typical of solids and liquids around us. Suppose we could narrow down the velocity of an aluminum sphere to within an uncertainty of1μmper decade. How small would it have to be for its position uncertainty to be at least as large as110%of its radius?

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